[Feature] HTTP based copy and paste functionality based on client's clipboard

### Expected Behavior

- When **Copy** (Ctrl+C) is triggered, the system clipboard content should be sent to the client's clipboard.
- When **Paste** (not Ctrl+V) is triggered, the client's clipboard content should be sent at once.
- Server clipboard as fallback.
- Shouldn't rely on Nut.js for anything other than sending Ctrl+C and the client's clipboard content.

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`navigator.clipboard.writeText(text)` requires HTTPS, but TanStack doesn't support it yet https://github.com/TanStack/router/issues/4287.

So, we need to consider methods that don't require HTTPS.

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Provide a video showcasing that copy copies to mobile clipboard (i.e., copying from server and pasting on mobile) and paste pastes from mobile clipboard (i.e., copying on mobile and pasting on server).